Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
118 views
in Permutations by (44.9k points)
closed by

How many 3-digit numbers are there when a digit may be repeated any numbers of time?

1 Answer

+1 vote
by (42.8k points)
selected by
 
Best answer

Let Suppose 3 digit number as 3 boxes as shown below. First Box is at 100th place, the Second box is at 10th place, and the Third box be at 1st place.

To make a3 digit number, 

1st box can be filled with nine numbers(1, 2, 3, 4, 5, 6, 7, 8, 9) if we include 0 in 1st box then it become 2 digit number(i.e 010 is 2 digit number not 3 digit) 

2nd box can be filled with ten numbers(1, 2, 3, 4, 5, 6, 7, 8, 9, 0) as repetition is allowed. 

Similarly 3rd box can be filled with ten numbers(1, 2, 3, 4, 5, 6, 7, 8, 9, 0) 

Total number of ways is 9 x 10 x 10 = 900

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...